Formation Control with Triangulated Laman Graphs

Formation control deals with the design of decentralized control laws that stabilize agents at prescribed distances from each other. We call any configuration that satisfies the inter-agent distance conditions a target configuration. It is well known that when the distance conditions are defined via a rigid graph, there is a finite number of target configurations modulo rotations and translations. We can thus recast the objective of formation control as stabilizing one or many of the target configurations. A major issue is that such control laws will also have equilibria corresponding to configurations which do not meet the desired inter-agent distance conditions; we refer to these as undesired equilibria. The undesired equilibria become problematic if they are also stable. Designing decentralized control laws whose stable equilibria are all target configurations in the case of a general rigid graph is still an open problem. We propose here a partial solution to this problem by exhibiting a class of rigid graphs and control laws for which all stable equilibria are target configurations

Consensus with Linear Objective Maps

A consensus system is a linear multi-agent system in which agents communicate to reach a so-called consensus state, defined as the average of the initial states of the agents. Consider a more generalized situation in which each agent is given a positive weight and the consensus state is defined as the weighted average of the initial conditions. We characterize in this paper the weighted averages that can be evaluated in a decentralized way by agents communicating over a directed graph. Specifically, we introduce a linear function, called the objective map, that defines the desired final state as a function of the initial states of the agents. We then provide a complete answer to the question of whether there is a decentralized consensus dynamics over a given digraph which converges to the final state specified by an objective map. In particular, we characterize not only the set of objective maps that are feasible for a given digraph, but also the consensus dynamics that implements the objective map. In addition, we present a decentralized algorithm to design the consensus dynamics

Distributed Evaluation and Convergence of Self-Appraisals in Social Networks

We consider in this paper a networked system of opinion dynamics in continuous time, where the agents are able to evaluate their self-appraisals in a distributed way. In the model we formulate, the underlying network topology is described by a rooted digraph. For each ordered pair of agents $(i,j)$, we assign a function of self-appraisal to agent $i$, which measures the level of importance of agent $i$ to agent $j$. Thus, by communicating only with her neighbors, each agent is able to calculate the difference between her level of importance to others and others' level of importance to her. The dynamical system of self-appraisals is then designed to drive these differences to zero. We show that for almost all initial conditions, the trajectory generated by this dynamical system asymptotically converges to an equilibrium point which is exponentially stable

Optimization of corrosion inhibition of essential oils of Alpinia galanga on mild steel using Response Surface Methodology

The use of plant extracts as corrosion inhibitors has gained prominence as replacement for synthetic organic compounds. The plant natural products have been found to be effective, cheap and eco-friendly anticorrosion agents. Corrosion inhibitions of essential oils of Alpinia galanga were investigated on mild steel in hydrochloric acid solution using weight loss method. The interactive effects of inhibitor concentration, temperature and time were optimized for maximum response of inhibition efficiency using Response Surface Methodology with Central Composite Design. The optimum inhibition efficiency of 88.5% at 775 ppm of inhibitor concentration, temperature of 320.4 K and reaction time of 3.75 hours was accomplished. The effectiveness of the inhibitor was also supported using scanning electron microscopy. The mechanism of interaction of both the inhibitor on mild steel surface was found to conform to the Langmuir adsorption isotherm

Chiral Modulations in Curved Space I: Formalism

The goal of this paper is to present a formalism that allows to handle four-fermion effective theories at finite temperature and density in curved space. The formalism is based on the use of the effective action and zeta function regularization, supports the inclusion of inhomogeneous and anisotropic phases. One of the key points of the method is the use of a non-perturbative ansatz for the heat-kernel that returns the effective action in partially resummed form, providing a way to go beyond the approximations based on the Ginzburg-Landau expansion for the partition function. The effective action for the case of ultra-static Riemannian spacetimes with compact spatial section is discussed in general and a series representation, valid when the chemical potential satisfies a certain constraint, is derived. To see the formalism at work, we consider the case of static Einstein spaces at zero chemical potential. Although in this case we expect inhomogeneous phases to occur only as meta-stable states, the problem is complex enough and allows to illustrate how to implement numerical studies of inhomogeneous phases in curved space. Finally, we extend the formalism to include arbitrary chemical potentials and obtain the analytical continuation of the effective action in curved space.Comment: 22 pages, 3 figures; version to appear in JHE

A note on a gauge-gravity relation and functional determinants

We present a refinement of a recently found gauge-gravity relation between one-loop effective actions: on the gauge side, for a massive charged scalar in 2d dimensions in a constant maximally symmetric electromagnetic field; on the gravity side, for a massive spinor in d-dimensional (Euclidean) anti-de Sitter space. The inclusion of the dimensionally regularized volume of AdS leads to complete mapping within dimensional regularization. In even-dimensional AdS, we get a small correction to the original proposal; whereas in odd-dimensional AdS, the mapping is totally new and subtle, with the `holographic trace anomaly' playing a crucial role.Comment: 6 pages, io

Pico-hydro electrification from rainwater’s gravitational force for urban area

The demand for electrical energy is increasing in most areas in the world. Unstable fossil fuel price and its rapid depletion have led to an intensive research on new energy source and energy conversion. This paper presents the performance of the energy harvesting which focuses on the experimental work to emulate energy harvesting from the rainwater by utilizing a Pico - hydro approach installed to a high building. NACuM core DB-370F DC generators, 1000 litres water tank, 0.5 inch diameter piping system used in two different configurations with three different head setups. The result shows a huge energy harvesting potential obtained from the system and rainwater with maximum 261 milliwatts despite the hardware’s limitation in the setup. Hance, contributes to the cost-efficient due to its small in size, environmentally friendly, and hassle-free maintenanc

A Policy Research Method Case-Study: Generating and Extracting Evidence-based Policy Inferences from a large EC Framework Programme Project

In 2004 the European Neighbourhood Policy (ENP) was instituted following the greatest single enlargement of the European Union (EU), to support security and peaceful relations between the EU and neighbouring countries with a unified governance approach to economic, social and political aspects of international cooperation. This paper reports on an effort to develop and test a methodology for bridging social science research and policy communities on an important policy question that concerns comity between the EU and its Eurasian, Middle Eastern and North African neighbouring countries1, although the approach applies to any broad policy issue for which multiple sources and types of research evidence are present. Five evaluative elements are developed and implemented whose complementary application result in a large set of policy inferences, a strategy of implementation, and researcher insights concerning the method. This case study suggests that the recommended evidence synthesis methodology has good potential for informing policy that is comprised of multiple elements, studied by large research teams, and enacted by diverse agents. The suggested methodology requires engagement by active researchers and policy experts in the formulation of policy options. It is put forward that improving the quality of evidence-informed policy will depend upon institutions and practices in the research and policy making communities. (authors' abstract)Series: SRE - Discussion Paper

Gross-Neveu Models, Nonlinear Dirac Equations, Surfaces and Strings

Recent studies of the thermodynamic phase diagrams of the Gross-Neveu model (GN2), and its chiral cousin, the NJL2 model, have shown that there are phases with inhomogeneous crystalline condensates. These (static) condensates can be found analytically because the relevant Hartree-Fock and gap equations can be reduced to the nonlinear Schr\"odinger equation, whose deformations are governed by the mKdV and AKNS integrable hierarchies, respectively. Recently, Thies et al have shown that time-dependent Hartree-Fock solutions describing baryon scattering in the massless GN2 model satisfy the Sinh-Gordon equation, and can be mapped directly to classical string solutions in AdS3. Here we propose a geometric perspective for this result, based on the generalized Weierstrass spinor representation for the embedding of 2d surfaces into 3d spaces, which explains why these well-known integrable systems underlie these various Gross-Neveu gap equations, and why there should be a connection to classical string theory solutions. This geometric viewpoint may be useful for higher dimensional models, where the relevant integrable hierarchies include the Davey-Stewartson and Novikov-Veselov systems.Comment: 27 pages, 1 figur

Views of the Chiral Magnetic Effect

My personal views of the Chiral Magnetic Effect are presented, which starts with a story about how we came up with the electric-current formula and continues to unsettled subtleties in the formula. There are desirable features in the formula of the Chiral Magnetic Effect but some considerations would lead us to even more questions than elucidations. The interpretation of the produced current is indeed very non-trivial and it involves a lot of confusions that have not been resolved.Comment: 19 pages, no figure; typos corrected, references significantly updated, to appear in Lect. Notes Phys. "Strongly interacting matter in magnetic fields" (Springer), edited by D. Kharzeev, K. Landsteiner, A. Schmitt, H.-U. Ye